Segal–Stolz–Teichner conjecture for supersymmetric field theories and TMF

Let $X$ be a space and let $n$ be an integer. Consider fully extended, degree $-n$, 2-dimensional supersymmetric field theories over $X$, modulo concordance. Segal–Stolz–Teichner conjecture. There is a $1\!:\!1$ correspondence

\left\{\begin{array}{l}\text{fully extended, degree $-n$, 2-dimensional}\\text{supersymmetric field theories over $X$}\end{array}\right\}\big/\text{concordance}\simeq \mathrm{TMF}^{-n}(X).

This conjecture expresses the proposal that supersymmetric Euclidean field theories furnish cocycles for generalized cohomology. The analogous assertion for complex $K$-theory is known in dimension $1$, whereas the $\mathrm{TMF}$ case remains open.